Fall 2015

** Organizers: Gennadi Kasparov, Ioana
Suvaina, ****Rares Rasdeaconu**

** Fridays,
3:10-4:00pm in SC 1310 (unless otherwise noted) **

**
Friday, September 25th
**

__Speaker:__** Tsuyoshi Kato,
Kyoto University**

__Title____:__** K-theoretic degree of
the covering monopole map** **
**

__Abstract__**: **I will present a
construction of K-theoretic degree of the covering monopole
map as a homomorphism between

full group C^* algebras.

Friday, October 9th

__Speaker:__** Rudy Rodsphon,
Vanderbilt University**

__Title____:__** Methods of cyclic
cohomology in index theory** **
**

__Abstract__**: **The aim of this talk
will be to review results in classical index theory through
the point of view of cyclic

cohomology, developed by Alain Connes as an alternative of de
Rham homology in Noncommutative Geometry.

We will then recall how it can be used to extend index theory
beyond the classical setting. As an introduction to a second

talk in two weeks, it will be elementary and accessible (I
hope) to graduate students. In particular, it should not
contain

recent results.

**Friday, October 23rd
**

__Speaker:__** ****Rudy
Rodsphon, Vanderbilt University**

__Title____:__** On Connes-Moscovici
transverse index problem ****
**

__Abstract__**: **This talk will be an
independent continuation of a previous talk two weeks ago. We
will sketch how

zeta functions and excision in cyclic cohomology may be
combined to obtain equivariant index theorems

for a certain class of hypoelliptic operators arising
naturally on foliations, actions being not necessarily proper.

As a corollary, we obtain a solution to a conjecture of Connes
and Moscovici, on the calculation of index classes

of transversally elliptic operators on foliations (without
holonomy). This is a joint work with Denis Perrot.

**Friday, October 30th
**

__Speaker:__** ****Anna
Marie Bohmann, Vanderbilt University**

__Title____:__** The Equivariant
Generating Hypothesis
**

** **__Abstract__**:
**Freyd's generating hypothesis is a long-standing
conjecture in stable homotopy theory. The conjecture

says that if a stable map between finite CW complexes induces
the zero map on homotopy groups, then it must

actually be nullhomotopic. I will formulate the
appropriate generalization of this conjecture in the case
where

a group G acts on the complexes and give some results about
this setting. In particular, I will show that the
rational

version of this conjecture holds when G is finite, but fails
when the group is S^1.

**Friday, November 6th
**

__Speaker:__** ****Anna
Marie Bohmann, Vanderbilt University**

__Title____:__** Constructing
equivariant spectra
**

** **__Abstract__**:
**Equivariant spectra determine cohomology theories that
incorporate a group action on spaces.

Such spectra are increasingly important in algebraic topology
but can be difficult to understand or construct.

I will discuss recent work with Angelica Osorno, in which we
build such spectra out of purely algebraic data

based on symmetric monoidal categories. Our method is
philosophically similar to classical work of Segal

on building nonequivariant spectra.

**Friday, November 13th
**

__Speaker:__** ****Spencer
Dowdall, Vanderbilt University**

__Title____:__** Surface bundles,
Teichmuller space, and mapping class groups**

__Abstract__**:** This talk will
introduce the mapping class group and Teichmuller space of a
surface with a

focus on how these objects are related to the theory of
surface bundles. We'll take the perspective of

Teichmuller space as a (sort of) classifying space for surface
bundles and explain how each surface bundle

gives rise to a monodromy representation into the mapping
class group. I'll then describe how the geometry

of Teichmuller space is related to the metric properties of
surface bundles, which will lead us to the notion

of convex cocompact subgroups of mapping class groups. The
talk will be introductory (and I hope

accessible!) in nature with the aim of setting the stage for a
follow-up talk discussing some of my work

in this area.

**Friday, November 20th
**

__Speaker:__** ****Spencer
Dowdall, Vanderbilt University**

__Title____:__** Hyperbolicity of
surface group extensions, and convex cocompact
subgroups of mapping class groups**

__Abstract__**:** Convex cocompact
subgroups of mapping class groups, as introduced by Farb and
Mosher, are subgroups

whose action on Teichmuller space is analogous to that of
convex cocompact Kleinian groups acting on hyperbolic

3-space. Moreover, it is exactly the convex cocompact
subgroups that give rise to Gromov hyperbolic surface

bundles and to hyperbolic extensions of free groups. In this
talk I will describe a setting, arising from hyperbolic

fibered 3-manifolds, in which there is a concrete connection
between these two notions of convex cocompactness

and explain how one may use this connection to prove certain
subgroups of mapping class groups are convex cocompact.

This is joint work with Richard Kent and Christopher
Leininger.

**Wednesday, December 2, 2015 (joint with the Topology & Group Theory
Seminar)
**

__Speaker:__ **Rares Rasdeaconu,
Vanderbilt University**

__Title:__ **Rational curves on real K3
surfaces **

Abstract: The simply connected complex
surfaces with vanishing first Chern class, also known as K3
surfaces, are

discussed from the perspective of their enumerative geometry.
Do such surfaces contain rational curves, i.e.

holomorphically immersed 2-spheres? If yes, how many?
Moreover, if the K3 surface admits an anti-holomorphic

involution, how many of these curves are invariant? I will try
to give some answers to such questions based on recent

joint work with V. Kharlamov.

**Friday, December 10th
**

__Speaker:__** ****Ioana
Suvaina, Vanderbilt University**

__Title____:__** Asymptotically
locally Euclidean Kahler surfaces, analytic
compactifications and classifications**

of ALE Ricci-flat Kahler surfaces, and I propose a classification of ALE scalar flat Kahler surfaces. The new techniques employed

are based on analytic compactifications and deformation theory.

Old Seminar Web-Pages: Fall 2009, Fall
2010